I want to solve the optimization problem
$$
\text{minimize }g(x) \quad \text{subject to} \quad \Vert x\Vert_{\infty}/\Vert x\Vert_{2} \le s
$$
for $x\in\mathbb{R}^d$ and $s\in(0,\infty)$.
The function $g$ is (strongly) convex and Lipschitz smooth.

I know, that I could probably try to find saddle points of the corresponding Lagrangian but I would like to know, if there is a faster or more elegant way.

Do you know of a similar problem, that has been considered before?